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Transcript
High-speed electrical sampling using optical second-harmonic generation
Ajay Nahataa) and Tony F. Heinz
Departments of Electrical Engineering and Physics, Columbia University, New York, New York 10027
James A. Misewich
IBM T. J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York 10598
~Received 15 January 1996; accepted for publication 29 May 1996!
We report the application of optical second-harmonic generation to the measurement of ultrafast
electrical pulses. The technique relies on the sensitivity of the second-harmonic response to electric
fields in centrosymmetric materials. Electrical pulses propagating on a silicon-based coplanar
transmission line have been characterized with subpicosecond time resolution and 100 mV/AHz
sensitivity. We have measured the bias dependence of the second harmonic intensity over a 20 V
range and have used this data to calibrate the transient response. The observed full-width at half
maximum response time of the SHG waveform is ;1 ps, which is consistent with the value obtained
from an electronic cross-correlation measurement. © 1996 American Institute of Physics.
@S0003-6951~96!03832-6#
The rapid progress in high speed electronic devices has
created the demand for new measurement technologies. For
maximum utility, these techniques must exhibit wide bandwidth, accurate signal reproduction, and minimal loading. In
response to this need, several ultrafast optoelectronic techniques have been developed.1 The first approach involved the
fabrication of photoconductively gated switches within the
device of interest.2 A number of other measurement methodologies including electro-optic sampling,3 photoemissive
sampling,4 and charge-sheet probing5 have also been devised. Electro-optic sampling has received particular attention since it is capable of providing picosecond temporal
resolution and submillivolt sensitivity. In the case of GaAs,
the electro-optic properties of the substrate itself may be exploited to perform in situ measurements.6 However, since the
dominant electronic material, silicon does not exhibit a linear
electro-optic effect, an external probe is necessary.
Optical second harmonic generation ~SHG! has been
shown to be an effective tool for studying surfaces of centrosymmetric media.7,8 A high degree of sensitivity to electric fields has been demonstrated in studies of semiconductors, both with fields applied normal to the surface and under
the influence of naturally occurring depletion fields.9–11 Recently, Lüpke et al. characterized the in-plane electric field
dependence in silicon using a transmission line structure.12
These investigations suggest the possibility of measuring
transient electric fields in high speed silicon-based devices.
In this letter, we demonstrate the first measurement of an
ultrafast electrical pulse by SHG. The method does not require any external probes or crystals. In the results presented
here, we have been able to detect an electrical pulse propagating on a transmission line with subpicosecond time resolution. In this approach, we expect the time resolution to be
controlled by the laser pulse duration down to an inherent
response time of less than 10 fs, while the spatial resolution
is limited only by the focusing of the probe beam.
We fabricated a coplanar waveguide structure, shown
schematically in Fig. 1, on silicon-on-sapphire. Since the
a!
Electronic mail: [email protected]
probing depth in the SHG measurements is short, the 0.6 mm
epitaxial silicon film may be considered equivalent to a bulk
sample. Ultrafast electrical pulses are generated on the transmission line by gating the upper photoconductive gap under
an applied dc bias. The SHG measurements were performed
at a nearby spot in the channel region straddling the center
conductor, while the electronic cross-correlation measurement required the inclusion of a second probe finger. The
channel regions on each side of the center line were 10 mm
wide and the photoconductive gaps were separated from one
another by 30 mm. The axis of the transmission line ran
parallel to the ~11̄0! direction of the epitaxial silicon. The
structure was formed by aluminum metallization using standard techniques. In order to reduce the carrier lifetime, the
device was implanted with two doses of O1 ions, 1015/cm2 at
100 keV followed by 1015/cm2 at 200 keV.13 We have found
experimentally that the ion implanation step significantly improves the ohmic nature of the contacts, as demonstrated by
the current voltage (I – V) characteristics ~not shown!.
The experimental arrangement is shown schematically in
Fig. 2. We used a 76 MHz mode-locked Ti:sapphire laser
operating at 800 nm with a pulse duration of 150 fs as the
optical source. Ultrafast electrical pulses were produced by
driving the upper photoconductive gap ~Fig. 1! with an average optical power of up to 70 mW. The pump beam was
directed onto the upper gap at normal incidence after passing
through a variable delay stage. The s-polarized probe beam,
FIG. 1. Schematic drawing of the coplanar waveguide transmission line.
The device consists of a center line with 10 mm wide channels on each side.
The black circles show where the pump and probe beams impinge on the
device.
746
Appl. Phys. Lett. 69 (6), 5 August 1996
0003-6951/96/69(6)/746/3/$10.00
© 1996 American Institute of Physics
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FIG. 4. The dependence of the s-polarized second harmonic intensity on the
applied dc bias for an s-polarized fundamental beam. The bias is applied
directly to the center conductor of the transmission line and the transient
field is probed in the channel region. The data are fit to a quadratic variation
of SH intensity with bias.
FIG. 2. Schematic drawing of the experimental setup.
with an average power of up to 100 mW, was incident on the
transmission line at 45° after passing through optical filters
to remove any second harmonic ~SH! photons. This beam
was focused to a spot size of approximately 10 mm and positioned at the center of the lower channel near the pump
gap. The device was oriented so that the axis of the transmission line lay in the plane of incidence of the probe beam.
Thus, the s-polarized electric field of the probe was perpendicular to the length of the channel and parallel to the dc
electric field. The reflected beam passed through several optical filters to remove the fundamental photons and an analyzing polarizer oriented to pass only s-polarized photons.
The SH photons were dispersed by a monochromator and
detected with a photomultiplier tube and photon counter.
We examined the temporal response of the device by
performing an electronic cross-correlation measurement. The
pump and probe gaps were each gated with an average optical power of 60 mW. The observed cross-correlation measurement with a bias of 10 V, shown in Fig. 3, has a fullwidth at half maximum ~FWHM! of 1.55 ps. The current,
i cc , measured as a function of the time delay, t, is given by14
i cc ~ t ! }
E
`
2`
g ~ t ! E tr ~ t2 t ! dt,
~1!
where g(t) is the gating function of the probe gap and E tr is
the transient electric field. We note that ideally E tr (t) should
be identical to g(t), ignoring dispersion and loss. The rise
time of g(t) is determined by the time integral of the laser
pulse and the carrier scattering time, while the decay time is
related to the carrier lifetime. The magnitude of g(t) is linearly proportional to the probe intensity. The asymmetry in
FIG. 3. The temporal waveform from a two gap electronic cross-correlation
measurement. The pulsewidth is 1.55 ps ~FWHM!.
the waveform may be attributed to the dissimilar nature of
the two photoconductive gaps. If we ignore the differences
between the gaps, the gating width ~FWHM! of a single gap
may be approximated by dividing the cross-correlation width
by A2 15 to obtain a value of 1.1 ps.
We initially measured the SH signal variation under the
application of a static bias on the transmission line. Since the
metal contacts to the silicon are ohmic in nature, because of
the ion implantation process, the applied bias and the dc
electric field scale directly with one another. The observed
SH intensity versus applied bias is shown in Fig. 4. The bias
dependence is fit to a parabolic form, with a vanishing minimum lying at the origin. We observed a shot noise limited
minimum voltage sensitivity of ;100 mV/AHz @corresponding to a minimum electric field sensitivity of 100 ~V/cm!/
AHz]. Several refinements that would significantly enhance
this sensitivity are discussed below. We estimate that the
average SHG power observed from the transmission line device with a 10 V bias, ;10 000 counts per second ~cps!,
corresponds to ;150 fW out of the device.
The bias dependence may be explained by considering
v)
the SH intensity at frequency 2v, I (2
, for s-polarized exss
citation and detection as a function of an applied dc field. If
we denote the coordinate perpendicular to the plane of incidence ~and the transmission line! by x, we may write7,12
2v!
2!
3!
2 ~v! 2
I ~x,x
} u k x ~s,xxx
1 x ~xxxx
E dc
x u @Ix # .
~2!
~3!
In this expression, x (2)
are the second-order nonlins and x
ear susceptibility of the surface and the third-order nonlinear
susceptibility of the bulk material, respectively. The usual
bulk second-order susceptibility has been omitted, since it
vanishes in centrosymmetric media such as silicon. The constant k is determined by the optical properties of the material
and the frequencies involved. For clarity, we have not explicitly included the contribution from the bulk nonlocal terms to
the second-order nonlinear response in the absence of a dc
field. Although an anisotropic term j may appear in this
measurement,7 it has, for our present purposes, a behavior
analogous to that of x (2)
s,xxx . The sensitivity of the SHG technique for probing electric fields arises from the fact that the
background is due to the second-order nonlinear response of
the surface and the nonlocal bulk terms only. In the current
measurement, these weak background contributions are ab-
Appl. Phys. Lett., Vol. 69, No. 6, 5 August 1996
Nahata, Heinz, and Misewich
747
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FIG. 5. Temporal waveform obtained using second harmonic generation.
The upper curve corresponds to the generation of an electrical transient by
the application of a 10 V bias across the pump photoconductor gap. The
lower curve is a reference scan obtained in the absence of an applied bias.
Both waveforms are offset from the origin for clarity.
sent, as demonstrated by the bias dependence minimum in
Fig. 4. The lack of a background SH response is due to the
amorphization of the silicon during ion implantation16 and
the well-established selection rule that an isotropic sample
will not produce an SH signal for s-polarized excitation and
s-polarized detection. We note that similar results may be
achieved with appropriately oriented crystalline silicon.12
We measured the transient electric field by placing a bias
on the gap of the pump photoconductor ~see Fig. 1! and
gating the corresponding photoconductive gap with an average optical power of 70 mW. The probe beam had an average optical power of 100 mW. The time-resolved SH intenv)
sity I (2
x,x for pump finger biases of 10 and 0 V is shown in
Fig. 5. Using the data from Fig. 4, we estimate that the peak
in the upper curve of Fig. 5 corresponds to a maximum voltage of approximately 500 mW on the center line. The width
of the temporal SH waveform was approximately 1 ps
FWHM. For an idealized measurement with an instantaneous
nonlinear optical response, the temporal waveform derived
from the SH intensity measurement may be related to the
time delay t by
I ~ 2 v !~ t ! }
E
`
2`
@ I ~ v ! ~ t ! E tr ~ t2 t !# 2 dt.
~3!
The intrinsic response time for such a measurement is limited by the spread in the arrival time of the probe beam
throughout the probed volume and the properties of the nonlinearity. Given the short escape depth ~125 nm! for the SH
signal and the expected electronic nature of the nonlinearity,
an intrinsic response time of ,10 fs may be expected. We
compare the results of the SH measurement with the electronic cross-correlation data. From the inferred single-gap
pulsewidth of 1.1 ps FWHM and an optical probe pulsewidth
of 150 fs FWHM, we obtain from Eq. ~3! a calculated pulsewidth for the SHG measurement of 0.9 ps. This is in reasonable agreement with the experimentally determined value.
In our current experimental arrangement, the photon energy of the probe beam lies above the band gap of silicon.
Thus, the probe beam produces both photocarriers and heat,
limiting the laser intensity that may be applied ~in our measurement, a laser power was chosen for which neither of
these effects appeared to be important!. A substantial improvement in the signal to noise ratio may, therefore, be
expected by using a photon energy for the probe lying below
the band gap of Si. In this case, the technique would remain
nonperturbative even for higher probe intensities. Since the
observed SH signal will still originate from the surface region of the silicon, the escape depth for the SH radiation
~which lies above the band gap! will remain short. Furthermore, significantly tighter focusing of the incident probe
beam, coupled with a reduction in the optical pulse duration,
will yield a substantial enhancement in the sensitivity.
In conclusion, we have demonstrated the detection of
picosecond electrical pulses using optical SHG in silicon.
Since the method exploits the nonlinear optical response of
silicon itself, it requires no additional probes or crystals and
is noninvasive. In this work, a detection sensitivity of 100
mV/AHz has been obtained with subpicosecond time resolution for an optoelectronically generated electrical transient
propagating on a coplanar transmission line. Further improvements in time resolution and sensitivity may be expected with refinements in the technique.
We thank Wei Xin for the use of his excellent mask and
Aniruddha Weling for many helpful discussions. A.N. is
grateful to D. H. Auston for his continued guidance and encouragement. This research was supported by the Air Force
Office of Scientific Research under Grant No. F49620-92-J0036.
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Appl. Phys. Lett., Vol. 69, No. 6, 5 August 1996
Nahata, Heinz, and Misewich
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